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Conferences are often organized within specialty disciplines, compartmentalizing information exchange by field of specialty. In the midst of these successful conferences there remains a niche for unifying, cross-cutting, interdisciplinary gatherings, where specialists can have exposure to diverse fields, a chance to meet new people in or near their individual areas of research, and participate in special sessions different from their own field. The proposed meeting of the 2nd International Conference on Mathematical Modelling and Computational Methods in Science and Engineering (ICMMCMSE-2020), has this purpose, to serve as a catalyst for computational mathematics among cutting edge applications in science and engineering.

The fields of Mathematical Modelling and Computational Methods and their applications to major areas such as Fluid Dynamics, Structural Mechanics, Semiconductor Modelling, Electromagnetics and CAD/CAM. Multidisciplinary applications of these fields to critical societal and technological problems encountered in sectors like Aerospace, Car and Ship Industry, Electronics, Energy, Finance, Chemistry, Medicine, Biosciences, Environmental sciences, Graph theory are of particular interest.

Computational mathematics, science and engineering are rapidly growing multidisciplinary areas with connections to business, economics, engineering, and mathematics and computer science through academia as well as industry. There is furthermore a constant need in these fields for the quick and efficient advancement of information exchange with an expert audience.

Altogether, the intent of this conference is to exchange information and to promote the transfer between the research community and industry consistent with the development and applications of computational methods in science and technology. So, the conference theme provides opportunity to initiate and develop such activities among the researchers, scientists and engineers from all over the world.

The overwhelming response to our call-for-papers indicates the popularity of this conference and confirms that the 2^nd ICMMCMSE-2020 has become the world-wide forum for all aspects of Mathematics and Computer Science in science and technology. There are totally 575 participants have been registered for the conference. Out of this, 315 have been registered and presented their research findings in the "Contributed Talk" sessions and rest of the 260 participants have been registered themselves as a Listener for the conference. Thanks to this response, all important fields of the 2^nd ICMMCMSE-2020 techniques, technology and exploitation are covered by their contributions. To our pleasure several Keynote and Invited sessions has been organised by eminent professors from USA, Turkey, Romania, UK, Thailand, New Zealand, UAE, Australia, some of the leading institutions in India like IIT's and IIST.

I would like to express my sincere thanks to all the authors for their outstanding contributions, sponsors for our conference RUSA 2.0, Elsevier Publishing Company, IOP Publishing Company, MDPI, AIMS Press and Hindawi Publishing House and in particular the members of the program board for their competent evaluation of the large number of submissions. Likewise, I would also like to express my appreciation to all the invited chairs for their careful preparation of the invited sessions.

Dr. R. Raja

Convener

2^nd ICMMCMSE-2020

List of Editors, Technical Editors, International Advisory Committee, National advisory committee members and this titles are available in this pdf.

List of Photographs available in this pdf.

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

● Type of peer review: Double-blind

The 2^nd ICMMCMSE-2020 review process starts with the Plagiarism check, if the paper is of less than 20% then it can be further sent out to review process, otherwise the authors were suggested to reduce the similarity to less than 20% and to encourage for resubmission as a first revision. After the completion of the similarity check, we transfer the article to the handling editor for further review process, normally we invite two reviewers to review the manuscript and give them a time schedule for a period of 3 months; then we allow the authors to revise the manuscript and give them 2 months period of time to resubmit their revised manuscripts.

● Conference submission management system:

Our Conference Paper submission system was totally managed by Conference Easy Chair.

● Number of submissions received: 206

● Number of submissions sent for review: 206

● Number of submissions accepted: 140

● Acceptance Rate (Number of Submissions Accepted/Number of Submissions Received X 100): 68%

● Average number of reviews per paper: 2

● Total number of reviewers involved: 2

● Any additional info on review process: In handling the review process for our Conference Proceedings, we have involved both the foreigners and as well as Indians for the double-blind review process.

● Contact Person for queries :

Name : Dr. R. Raja

Affiliation : Alagappa University, Karaikudi 630003, Tamil Nadu, India

Email : rajarchm2012@gmail.com

Streamline upwind Petrov-Galerkin (SUPG) stabilization for the virtual element discretization of the convection-diffusion equation produces local oscillations in the crosswind direction. To overcome such a shortcoming, an additional shock-capturing term is added into the formulation. In this paper, we propose a nonlinear shock-capturing technique and prove the existence and stability of the discrete solution. The resulted nonlinear system of equations is solved using a simple iterative technique. Numerical experiments are conducted to show the efficiency of shock-capturing term in reducing the spurious oscillations along the crosswind direction.

The modeling of air contaminant dispersion extended from the Gaussian plume model is proposed. This model takes onto account the transport of pollutants emitted from open biomass burning located on a complex terrain where the concentration behavior is modeled by the advection-diffusion equation in a stationary frame. In addition, the existence, uniqueness, and regularity of this problem are discussed. The discontinuous Galerkin method is employed for numerical treatments. Especially for numerical experiments, the propagation of air pollutants in the complex terrain areas in Chiang Mai province, Thailand, is investigated. Results of numerical experiments demonstrate the validity of the air pollution dispersion model.

In this paper, a prey-predator eco-epidemiological model with susceptible and diseased prey is constructed and investigated. The existence, uniqueness and boundedness of the solution of the system are studied. The conditions for the local and global stability of coexistence steady state are examined. At last, the mathematical results are interpreted with the help of numerical simulations.

This paper mainly focuses on a single server retrial inventory system. The arrival of customers follows the Poisson process, and when the inventory level depletes to the reorder level s due to service, replenishment order placed according to (s, Q) policy. The lead-time governed by an exponential distribution with parameter β. A customer who finds the server busy or inventory dry moves to an orbit of infinite capacity with probability σ. Customers in orbit independently tries to access the server at a rate of θ, which depends on the number of customers in orbit. A retrial customer returns to the orbit with probability δ if the server is busy or inventory is dry. Each customer in orbit generates priority according to an exponential distribution with rate γ. If the server is free, a priority generated customer will get immediate service. Else such a customer have to wait in a space A₁ of capacity one, which is reserved only for priority generated customers. The service times follows exponential distribution with different rates for ordinary and priority generated customers. The model turned out to be a level-dependent quasi birth-death(LDQBD) process, and we use Matrix-Analytic Method as a tool for obtaining a solution.

This paper presents a study of blow-up of solutions to a quasilinear p(x)-Laplacian problem related to the equation ${z}_{t}(x,t)={{\rm{\Delta }}}_{p(x)}z(x,t)+g(z(x,t))$ We use a condition on the nonlinear function g(z) given by, $\varsigma {\int }_{0}^{z}g(s)ds\le zg(z)+\eta {z}^{p(x)}+\mu,z\gt 0$ We extend the existing results on blow-up for a nonlinear heat equation to variable exponent case and establish an upper bound for the blow-up time with the help of concavity method.

A new structure called a fuzzy fibrewise (briefly ℬ) structure is propounded and contemplated in this disquisition. Also the perception of ℬ open (resp. closed) structures is introduced and some properties involving these concepts are investigated. Further, some of the significant separation axioms are studied in ℬ versions. Moreover, the concept of ℬ compactness is established.

A theoretical examination of the thermal convection for a couple stress fluid which is electrically conductive and possessing significant thermal relaxation time with an externally applied magnetic field is carried out. Fourier's law fails when fluids are subjected to rapid heating or when it is confined and in the case of nano-devices. A frame invariant constitutive equation for heat flux is considered. The linear analysis is carried out implementing a normal mode solution and the non-linear stability of the system is analyzed using a double Fourier series. The analysis of the transfer of heat is determined in terms of the Nusselt number.

Accurate transmission of a message is always of prime importance in day-to-day life. Messages of paramount importance require greater caution while transmission, so that it is not disrupted by any means. But due to several problems there may be some sort of misinterpretation on the received message. Based on the above mentioned factors, in this paper, a new idea of the Unique Decipherability of Fuzzy Codewords, their decomposition and the ambiguity of fuzzy codewords based on their relative weight are proposed, which handles several special issues in Information Theory.

Over the past two decades, constrained quantum systems have arisen to be a field of considerable importance in physical, chemical and biological sciences. In this work, we have investigated the behavior of a confined H atom inside a harmonic environment: $V(r)=-\frac{1}{r}+{(\frac{r}{{r}_{c}})}^{2}$. The eigenvalue equation is solved using a generalized Legendre pseudospectral method, which offers an optimal, non-uniform spatial discretization. By means of a symmetrization technique and a non-linear mapping, a symmetric eigenvalue equation is obtained. A detailed energy analysis reveals that (a) for all the states, energy values decrease with growth in confinement radius, r_c (b) for fixed number of nodes, it grows with rise in l, and (c) at a fixed n, it decreases with progress in l. Interestingly, the energy arrangement of various quantum states is found to be very different from that in a free H atom. A general rule has been proposed to understand the energy ordering pattern. Furthermore, we have analyzed some information-based quantities like Shannon information entropy, Fisher information and Onicescu energy, in position and momentum spaces for this soft, impenetrable stressed system. These are examined with respect to r_c as well as n, l quantum numbers. Additionally, the Compton profile and Compton entropy have also been explored here.

A radio coloring of graphs is a modification of the frequency assignment problem. For a connected simple graph G, a mapping g of the vertices of G to the positive integers (colors) such that for every pair u and v of G, |g(u) −g(v)| is at least 1 + diam(G) −d(u, v), is called a radio coloring of G. The largest color used by g is called span of g, denoted by rn(g). The radio number, rn(G), is the least of {rn(g) : g is a radio coloring of G}. In this paper, for n ⩾ 7 we obtain the radio number of Cartesian product of complete graph K_n and cycle C_m, K_n☐C_m, for n even and m odd, and for n odd and m 5 (mod 8).

The effect of exothermic chemical reaction of zero-order on Bénard-Darcy ferroconvection is investigated using the technique of small perturbation. The eigenvalues associated with an adiabatic lower wall are determined by employing the Galerkin method. The Darcy-Rayleigh number is computed in terms of the parameters pertaining to chemical reaction and ferromagnetic fluid. It is established that, when chemical reaction escalates, there is a considerable shift from linearity and occurrence of asymmetry in the basic temperature profiles. It is ascertained that the threshold of Bénard-Darcy ferroconvection is augmented through the stresses of both mechanisms due to chemical reaction and magnetization, and the ferroconvective instability due to nonlinearity of magnetization is rather inconsequential when chemical reaction is present. It is also shown that the destabilizing feature of magnetic forces resulting from the fluid magnetization is less pronounced when chemical reaction is present.

In this Research article the authors investigate minimum domination, neighbor-hood and Laplacian energy value of the line graph of IEEE-14 bus system in electric power networks. This paper presents a graph theoretic approach to solving the problem of placement of observations for the estimation of power system status. Estimation parameters for the IEEE 14 bus system. In this paper, a novel technique based on iterative stability-restricted optimum flow of power is suggested.

Mathematical Modelling and Big-data Analytics are playing a vital role in educational databases. The result of integrating technology to predict student performance along with Mathematical Modelling and Big-Data Analytics helps us to make better decisions about teaching and learning. Modelling involves formulating real-life situations or to convert the problems in mathematical explanations to a real or believable situation. However, Mathematical modelling are an essential enabler in Big-data and Developments in Big-data analytics require not only more computing, but also new advanced mathematical approaches. In this paper, our main aim to see how Mathematical Modelling and Big-Data analytics help in students' learning and how they relate to each other.

A graph is a representation of a relation between a pair of objects in a set called vertex set. A relation is a set of two-element subsets of the vertex set, called edge set. If the restriction of the two-element subset is relaxed to any number, the corresponding representation is a hypergraph. An r-uniform hypergraph is a Steiner system, in which every pair of nodes is contained in exactly a single edge. Knodel graphs, Fibonacci graphs, and r-partite complete graphs are structures with optimal communication properties. Knodel hypergraph and Fibonacci hypergraph are introduced. Partitioning of the edge set leads to the decomposition of a given graph into sub-structures. If all such sub-structures are isomorphic, the decomposition is an isomorphic decomposition. The isomorphic decomposition of an r-partite hypergraph, Knodel hypergraph, and Fibonacci hypergraph into hyperstars are presented.

Nipah virus spreads from human to human at a fast pace by contact. It has been realized that very close contact for a long period or direct exposure to excretions of diseased can cause the spread of the virus from one person to another. So avoiding contact with infected is very crucial in the control and eradication of the disease. Getting information about infection in the early stage is an important factor in the planning of isolation of infected and suspected. The contact pattern of humans in society makes a network of individuals. Dynamics of social networks have become a focal point in the mathematical study of the spread of disease in recent years. In normal situations, an individual comes in contact with others due to many reasons. We have contact with our family members, relatives, and friends. We come in contact with others by chance when we are in public places. In the paper, we analyze the recent Nipah outbreak in Kerala and explain the dynamics based on social network analysis. The paper aims to bring into light the importance of a network-based analysis of the infected immediately after the outbreak of the disease. The contact pattern must be closely analyzed to decide who should be quarantined and observed.

This article studies a perishable inventory system with a production unit. The production process is governed by (s, S) policy and it is exponentially distributed. The primary arrival follows Markovian arrival process(MAP) and the service time is phase-type distributed random variable. The inventoried items are subject to decay exponentially with a linear rate. A newly arriving customer realizes that system is running out of stock or server busy either moves to infinite waiting space with a pre-assigned probability or exit system with complementary probability. Customers in the waiting space make retrials to access the free server at a linear rate. If the system is running out of stock or the server is busy upon retrial, customers go back to orbit with different pre-defined probabilities according to the level of inventory or exit the system with corresponding complementary probabilities. The system is analysed using Matrix Analytic Method(MAM) and the findings are numerically illustrated.

The scheme of small perturbation is used to address the problem of buoyancy driven convection of Darcy-Brinkman type in a ferromagnetic fluid invoking the Maxwell-Cattaneo law. An analytical solution of the eigenvalue problem involved, encompassing stationary and overstable modes, is obtained by adopting simplified boundary conditions. The mathematical application package MATHEMATICA is adopted to determine the eigenvalue expressions and the critical numbers. It is established that the threshold of Darcy-Brinkman ferroconvection is amplified through the stresses of magnetic and second sound mechanisms and the opposite influence is found to be true due to the presence of porous medium. It is delineated that both the critical frequency of oscillations and aspect ratio of cells of convective heat transfer are susceptible to the different parameters of the study. It is also shown that, as long as the Cattaneo and Prandtl numbers are pretty high, the oscillatory mode of instability is preferred to the stationary mode of ferroconvection.

In this article, we analyze the finite capacity Markovian queueing model with working breakdowns and a two-phase service. The server provides the primary service as well as the secondary elective service. The cost optimization problem is to find out the minimum cost per unit time by a direct search method to optimize service rates.

This paper considers an (s, S) inventory system with production in which demand occurs according to a Bernoulli process and service time follows a geometric distribution. The maximum inventory that can be accommodated in the system is S. When the items in the on-hand inventory are reduced to a pre-assigned level of s due to service, production is started. The production time follows a geometric distribution. The production process is stopped as soon as the inventory level reaches the maximum. Customer who arrives during the inventory level is zero is assumed to be lost. Using the stochastic decomposed solution obtained for the steady-state probability vector, we analyzed the inventory cycle. A suitable cost function is defined using the performance measures. Numerical experiments are also incorporated to highlight the minimum value of the cost function against the parameter values.

In this paper we have found composition product of two paths using Inverse majority neighborhood number parameter.

In broadcasting and gossiping, communication structures are modelled using graphs. In simplex model, a communication link sends messages in a particular direction. The simplex network is modelled by directed graphs. Certain Knodel graphs are optimal broadcast graphs. This article defines the two layer representation of Knodel digraphs and Fibonacci digraphs-both are symmetric regular bipartite digraphs. A Knodel digraph is a symmetric digraph produced by replacing each edge of an undirected Knodel graph by a symmetric pair of directed edges. A Fibonacci digraph is a symmetric digraph produced by replacing each edge of an undirected Fibonacci graph by a symmetric pair of directed edges. Decomposition of a given graph is the partitioning of edge set so that the given graph is split in to sub-structures. If all such sub-structures are isomorphic, the decomposition is isomorphic decomposition. The isomorphic decomposition of the Knodel digraphs and Fibonacci digraphs in to isomorphic paths and stars is presented. The star decomposition of both Knodel digraph and Fibonacci digraph leads to the decomposition of equi-bipartite complete digraphs in to two classes of stars.

A set S⊆ V(G) said to be an at most twin outer perfect dominating set if for every vertex v∈V-S, l⩽|N(v)∩S|⩽2 and < V-S> has at least one perfect matching. The minimum cardinality of at most twin outer perfect dominating set is called the at most twin outer perfect domination number and γ_atop(G) denotes this number. This was initiated by G.Mahadevan.et.al., recently. Here we find this number for general Binary-tree. corona product of paths and cycles and lotus inside graph.

In Double Layered Fuzzy Graph, it is discussed that, the Fuzzy Vertex Colouring, Fuzzy Edge Colouring, Fuzzy Total Colouring and determined bounds for Fuzzy Chromatic Number, Fuzzy Edge Chromatic Number and Fuzzy Total Chromatic number. Also established some of the Domination parameters such as Fuzzy Dominator Chromatic Number, Inverse Domination, Connected Inverse Domination.

In this paper hexagon hesitant fuzzy set is used to solve the higher order uncertainties with TOPSIS method. Hexagon Hesitant Fuzzy Multi Attribute Decision Making problems faced by the farmer who plant monsoon crops in Villupuram District.

In this analysis, a theoretical model is proposed to examine the collective effect of slip velocity, magnetic field, and inclination angles on an unsteady non-Newtonian particulate suspension flow in an inclined diseased tapered tube with a porous medium by applying an external inclined magnetic field. By deploying integral transform methods, analytical expressions are obtained for the flow characteristics such as velocity profiles of fluid and particles, wall shear stress, flow rate, and flow resistance. With the aid of numerical computations, the significance of inclination angle, porous medium, and magnetic intensity are analyzed and illustrated graphically. Further, various physiological parameters affecting the flow characteristics are discussed which would facilitate the rheological functions of blood in the field of biology, biomedicine, and engineering sciences.

In this paper, we present the Atangana Baleanu fractional derivatives of some special functions such as trigonometric, exponential and hyperbolic functions. The AB fractional derivatives are calculated using the formula for RL derivatives and are calculated for all functions which belong to L¹ [a,b]. The importance of these derivatives comes from the fact that certain dissipative phenomena cannot be explained using classical fractional operators.

The Internet of Things (IoT) defined as the assembling of real-world objects that are connected over the Internet to make human lives become well-being. The implementation and success of an IoT depend on how it's secured. But providing security is a critical task because of various natures of IoT devices such as shared and open environment, a wide range of communication protocols, standards, self-organized, lack of central control, heterogeneity of devices, etc. To provide security solutions and mechanisms, key management, cryptographic mechanisms such as private and public-key cryptography, Intrusion Detection System (IDS), and hash functions have been used. Though it is working well, it is not suitable for lightweight IoT devices. Because of such mechanisms always demand high computational, memory, and processing. To overcome these issues, researchers have chosen trust management for providing security. In this article, some of the trust-based solutions have presented. Besides, security issues, security loopholes/attacks in various layers of IoT, security requirements, trust management in IoT, properties of trust, trust management building blocks, the role of trust management in IoT, basic trust calculation methods have presented.

The connected domination polynomial of a connected graph G of order n is the polynomial ${D}_{c}[G,x]=\sum _{i={\gamma }_{c}}^{n}{d}_{c}(G,i){x}^{i}$, where d_c(G, i) is the number of connected dominating sets of G of cardinality i and γ_c(G) is the connected domination number of G [5]. In this paper we find the polynomial D_c(G, x) for some constructive graphs.

This examination is passed on to decide the properties of three-dimensional flow of H₂O/NaC₆H₉O₇ base liquid with F e₃O₄/Al₂O₃ nanoparticles confined by a Riga plate. Mathematical model is detailed as PDEs and afterward transmuted into ODEs with the assistance of similarity transformations. The subsequent system is numerically dealt with the aid of the Runge-Kutta procedure bolstered by shooting technique. Highlights of the flow field and thermal field are exemplified quantitatively through plots. Results for the local skin friction coefficient and local Nusselt number are registered and examined tabularly. It is induced that the modified Hartmann number and stretching ratio parameter ameliorate the velocity profile. Additionally, it is likewise explained that H₂O−Al₂O₃ nanofluid has high skin friction values and the rate of heat transfer of NaC₆H₉O₇−Al₂O₃ nanofluid is more desirable.

The Queuing model introduced here defines a batch arrival model with the extra assumption of stages of service. In addition, the system deploys a set up time stage for the pre-processing work to be carried out, which is essential for the stages of service. In addition, we introduce a new factor Reneging that occurs twice in this model during the setup time stage and also during the t7]=, ZO, WZ]pu[sZry, v(W(t7ZJi, RustZ]=r's, (rr7v([, follows a Poisson distribution, while the service rendered follows a general distribution. Here, we carry out the concept of Compulsory vacation as a maintenance work duration, which helps to reduce the occurrence of service interruption. The model is well elucidated with thermo pack process from mechanical engineering. Thermo pack is the machine that is used as a boiler. Generally, we raise the temperature of oil in the thermo pack. The working principle of the thermo pack is similar to that of an ordinary boiler. It can raise the temperature of the oil from the initial temperature along with the temperature of oil which has been already used once. After the production of hot oil, it is allowed to flow around the mould to keep up the temperature inside the mould. In other cases, this oil can also be used for refining purposes. Nowadays, recent advancements in the thermo pack have led to the creation of new and advanced small size thermo pack for small-scale production. The procedure completed in this structure is considered through Queuing hypothesis. The above process comprises queuing parameters like set up time, stages of process, compulsory vacation process and the concept of types of Reneging. The Queuing issue emerges in the above auxiliary technique is understood by valuable variable strategy. The probability of creating capacity of the line size, duration of line, the number of clients in the framework, holding up time of the clients in the line just as in the framework, usage factor and the inert time of the server are inferred. Numerical delineation and a broadened graphical assessment are undertaken around the conclusion to help the model.

In this paper, Greedy Algorithms such as Kruskal's, Prim's, Boruvka's, Reverse-delete Algorithm were applied on different types of graphs like Mobius-Kantor graph, Durer graph, Golomb graph to find the (MST).

The main aim of this paper is to find the critical path by using triangular fuzzy numbers, Fuzzy total float, free float and Independent floats are introduced and we discussed this with the suitable examples.

The paper comprises an (s,S) production inventory facility in which multiple vacations and varying service rates are considered for the multiple servers. The arrival of customers constitutes a Markovian Arrival Process (MAP) and service completion times follow the phase type distributions with representations ( α, S) and ( β, T ) respectively. Manufacturing needs to begin at the moment when the stock position falls to s. Service is offered at a lower rate if the stock level ranges from 0 to s and the service time distribution has the representations (α, η₁S) and (β, η₂T ), 0 <η₁, η₂< 1 respectively. If the stock level reaches the maximum S, production is ceased to operate. 1-limited service policy, Bernoulli service schedule, and Exhaustive service disciplines are considered for the servers. A suitable cost function is outlined as per performance assessment. The impact of negative correlated inter arrival times on cost function is illustrated. Also, a relative study of expected cost function on different service modes is presented.

Now a day's many organizations have struggled in how to minimize the employer training cost. Consider the assignment problem for each assigning workers with their own skill set, to task which demand different skills in an efficient manner. It's a challenging problem that often requires workers to receive additional training. The training of workers is very costly of the employee training in the world. So, in this paper we analyze and minimize the entire training cost. A numerical example is included.

Diabetes, a fifth leading disease in terms of causing death, is a complex syndrome, characterized by the altered metabolism of proteins, fats, and carbohydrates result in the raising of blood glucose level to more than 180 mg/dl cause a condition called Hyperglycemia. Many shreds of evidence are suggesting the positive relationship between diabetes and cancer means diabetic patients are more prone to cancer. Risk factors associated with type 2 diabetes and cancer share some common pathophysiologies as well as treatments and thus type-2 diabetes mellitus may be a predisposing factor for Cancer. The work proposes a generalized mathematical model whose numerical solution depicts the risk of cancer to the one having type-2 diabetes mellitus. In type-2 diabetes, the body neglects to react to the insulin produced by the body itself. A system of differential conditions is utilized for depicting these changes. This model incorporates the concentration of glucose, insulin and cancer growth cells. Taking everything into account, the possibility of having cancer is more in the individuals having longstanding type-2 diabetes than those who do not have diabetes. In the work, we propose a numerical model for the risk of disease to a patient having type 2 diabetes mellitus for quite a while.

The achieved sufficient conditions for nonexistence of so-called Kneser solutions are based on the new comparison principles, which help us decrease the problem of the wavering between the third and first-order equations. Examples are given to prove the significance of new theorems.

The graph G₁, G₂ G₃ and G₄ which is defined by the direct sum of four fuzzy graphs G₁⊕G₂⊕G₃⊕G₄ Tins is also proved the effective values. The degree of the vertices is G₁⊕G₂⊕G₃⊕G₄ is calculated with the establishment of the regular property and the Connectedness of the Direct Sum of four Fuzzy Graphs.

Results of any working out are of practical use only if statistics about their accuracy is also available. This is commonly correct in the molecular and drug design where the accuracy in each model is of vital importance. Valuation of the efficiency of changes presented in a prototypical and quantifiable evaluation of the presentation of changed models necessitates quantity for calculating the full uncertainty in designing the drug molecules, the collective impact from all improbability causes. To novelty, such a quantity is some of the points of our research. In the fuzzy model, the consequent of the fuzzy rule is often determined with degrees of belief or credibility because of vague information originating from evidence not strong enough and "lack of specificity". In this paper, we present a fuzzy model incorporated with the fuzzy Dempster-Shafer Theory. A well-known example of drug dosage prediction is tested, the prediction results show that our fuzzy modeling is very efficient and has a strong expressive power to represent the complex system with uncertain situations.

In this paper, using Neighbourly Irregular Fuzzy Graph and Neighbourly Irregular Chemical Graph, we introduce Neighbourly Irregular Fuzzy Chemical Graphs(NIFCG). We also discuss about the Total Irregular value for Double Layered Neighbourly Irregular Fuzzy Chemical Graphs(NIFCG) using edge cut method.

In this paper, we studied domination of a Triple layered fuzzy graph, Complement of a Triple layered fuzzy graph and Complete Triple layered fuzzy graph and established bounds for the same graphs.

A singularly perturbed boundary value problem for a linear parabolic second order delay differential equation of reaction-diffusion type with discontinuous source term is considered in the rectangle domain Ω = {(x, t) : 0 < x < 2,0 < t ⩽ T}. Discontinuity occurs in the source term at (d, t) < ∈ Ω. As the highest order space derivative is multiplied by a singular perturbation parameter, the components of the solution exhibit boundary layers at (x,t) = (0,t) and (x,t) = (2,t) and interior layers at (x, t) = (1, t) and/or at (x,t) = (d,t) and (x,t) = (1 + d, t) with respect to the position of (d, t) in Ω. A numerical method which uses classical finite difference scheme on a Shishkin piecewise uniform mesh is suggested to approximate the solution. The method is proved to be first order convergent uniformly for all the values of singular perturbation parameters. Numerical illustrations are presented so that the theoretical results are supported.

In this paper, we analyze the waiting time in two stage preemptive priority queueing system. The service time considered here is k-phase Erlang distribution. We have assign the priority server to the emergency customer without affecting the regular priority unit. It is possible only if the servers are independent. In this case, we derive the steady state probability of the waiting time customers in ordinary and priority unit. A numerical example is included.

This paper proposes an efficient hybrid analytical method named the Generalized Homotopy Analysis Method (GHAM) for solving nonlinear differential equations. The proposed hybrid method consists of topology based Homotopy Analysis Method (HAM) and Laplace typed integral transform (G-transform). Compared with HAM, GHAM does not require the effort to perform repeated integration and differentiation, when it is applied to solve higher order differential equations. Compared with G-transform, GHAM serves as an effective approach to tackle higher-order nonlinear differential equations. The effectiveness of GHAM is illustrated through the analysis of numerical examples, and the obtained results are graphically depicted. Also, GHAM is effectively utilized to analyze the density of the forest cover incorporating various parameters, which include the seed reproduction, seed deposition, seed establishment rates, old trees due to aging and the coefficients of mortality due to space variables.

Let D be a digraph of order p and size q. For an integer k ⩾ 1 and ν ∈ V(D), let $\sum _{e\in {E}_{k}(v)}f(e)$ where E_k(v) is the set of all in-arcs which are at distance at most k from ν. A V_k-super vertex in-magic labeling (V_k-SVIML) is an one-to-one onto function f : V(D) ∪ A(D) → {1,2..., P + q} such that f(V(D)) = {1,2..., p} and for every ν ∈ V(D), f(ν) + ωk(ν) = M for some positive integer M. A digraph that admits a V_k-SVIML is called V_k-super vertex in-magic (V_k-SVIM). In this paper, we study some properties of V_k-SVIML in digraphs. We characterized the digraphs which are V_k-SVIM. Also, we find the magic constant for E_k-regular digraphs. Farther, we characterized the unidirectional cycles and union of unidirectional cycles which are V₂-SMM.

We describe a mathematical model for the interaction between three species consists a prey (x₁) and two neutral predators (x₂, x₃), surviving on the common prey (x₁). Here all the three species have limited their own natural resources. The system is explained by couple of differential equations. The co-existing state is identified and also characterized the local and global stability analysis at this state. The dynamical behaviour of the system is studied using Numerical simulation. It is shown that the system is globally asymptotically stable.

In this paper, we consider an M/M/1/N queue with working breakdown and two types of server vacations. Sensitivity analysis of the model is performed to aissue with the point of streamlining service rates by limiting the normal expense per unit time using the direct search method.

This paper addresses the stabilization of Takagi-Sugeno (T-S) fuzzy systems with time delay. In particular, the control system with parameter uncertainties are modeled through an interval type-2 (IT2) T-S fuzzy model, in which the uncertainties are handled via lower and upper membership functions. By developing some new techniques, a fault-tolerant controller is designed to ensure that the closed-loop fuzzy time-delay system is asymptotically stable with nonlinear fault input. Finally, a numerical example that demonstrate the effectiveness of the proposed conditions are provided.

In this paper, the concepts of multiset Boolean filter, multiset Boolean pseudofilter, anti-multiset Boolean filter, and anti-multiset Boolean pseudofilter are introduced. Also, the relation between multiset Boolean filter(pseudofilter) and some other types of multiset filters(pseudofilters) are given.

In this paper, we analyze the system performance in FM/FM^(k)/∞ using Estimation theory. Initially, we convert Erlang queueing system into fuzzy Erlang system, using Alpha – cut method and obtain different possible values of^α. Finally, using Robust ranking method it's helpful to measure the defuzzification values and analyzes the unique optimization of system performance.

The sequences of Fibonacci words plays an important role in formal language theory and combinatorics on words. Fibonacci partial words, arrays and their combinatorial properties such as palindromes and primitivity was established. In this paper, we extend some fundamental results about Fibonacci words to Fibonacci partial words such as compatibility, periodicity and also binary correlations which turns out to be an effective technique of portraying sets of periods of Fibonacci partial words briefly with comprehensive scope.

The iterates of Fuzzy Neutrosophic Soft Circulant Matrices (FNSCMs) under the max-min product is examined right now. It is indicated that on the off chance that the first row of a FNSCM is in decreasing order, at that point the iterates of the circulant converge and on the off chance that the first row is in increasing order, at that point the iterates oscillate.

In this paper, the idea of fuzzy Fuzzy α-Ψ*-Convergence Spaces-filters on fuzzy Fuzzy α-Ψ*-Convergence Spaces-open sets and fuzzy Fuzzy α-Ψ*-Convergence Spaces-convergence spaces are presented. Typically, the description of fuzzy minimal prime Fuzzy α-Ψ*-Convergence Spaces-filters in a fuzzy topological space is explored. Likewise, the ideas of fuzzy Fuzzy α-Ψ*-Convergence Spaces-regular convergence spaces and fuzzy weakly Fuzzy α-Ψ*-Convergence Spaces-regular convergence spaces are initiated and few of their captivating properties are examined.

This paper aims to present improved result of dissipativity analysis in Markovian switched neural networks with time-delays. By applying the novel extended reciprocally convex matrix inequality with the construction of Lyapunov- Kravsovskii functional and by using the linear matrix inequality technique, a set of sufficient conditions has been established to guarantee the existence of analysis. Numerical example with simulation is illustrated for the effectiveness of the proposed method.

Certain special forms of self-similar solutions which satisfy Khokhlov-Zabolotskaya-Kuznetsov equations or a generalized Burgers equation in (1 + 2)-dimensions are reported.

Given a graph G, b coloring seeks a proper coloring of G with the descriptive property that every color class in the graph contains a dominating vertex. We have to minimize the number of colors in proper coloring. In this paper, we show how chromatic and b-chromatic number of a graph changes with the graph operators and relation between chromatic and b-chromatic number has been explored.

For the tensor product of paths, inverse majority neighborhood number n_m⁻¹ (G) of G are determined in this paper. Also obtained some bounds for G = P_n ⊗ P_m.

In this paper, several characterizations of fuzzy soft regularly nowhere dense sets, fuzzy soft regularly dense, fuzzy soft regularly residual, several examples are given to illustrate the concepts introduced in this paper.

In this article, we obtain several comparison theorems for the second-order neutral differential equation $\frac{d}{dt}(r(t){(\frac{d}{dt}z(t))}^{\gamma })+{q}_{1}(t){x}^{\lambda }(\sigma (t))+{q}_{2}(t){x}^{\beta }(\eta (t))=0$, t ⩾ t₀, where γ, λ, β are ratios of positive odd integers. We compare above equation with the first-order differential inequalities in the sense that the absence of the eventually positive solutions of these first-order inequalities implies the oscillation of the studied equation.

This study aims to find the ultimate solution for the table to be used by different kinds of people, such as a healthy kid, young, old, and physically disabled. People face problems while using the table of inappropriate height. Especially, physically disabled people are unable to cope with healthy while doing regular work due to height constraints. Using a human-centered design approach, the authors create a design process based on field research and catering to local needs to develop a suitable product for users in a developing country. So, the authors introduced a table, which has a motorized height adjusting mechanism. Ultrasonic sensors detect the user's height and height of the table adjusted as per the height of the user.

The present paper examines the working and reliability of a pair of a two-unit cold redundant system in a pharmaceutical agency. Initially, out of two units, one unit is operative and the other unit acts as a cold redundant. On the failure of the working unit, the redundant unit is put to work. As the demand varies, the manufacturing of the product is also very much affected and so the machines may need to put into the rest period when the vast range of manufacturing is in the distinction to those demanded. It leads to a decline in the warranty period of the product. Additionally, another factor of the preventive/corrective maintenance (PM/CM) is also taken into the consideration. The main aim is to an evaluation of the expected rest period and expected PM/CM period and to determine the maximum profit gained by the company using the Markov process and regenerative technique. The authors have calculated various measures of the system's effectiveness. Numerical consequences and graphs of a precise case are additionally included.

This research paper presents the idea of energy for pebbling graphs. Pebbling is transportation of two pebbles from one vertex (place) to another vertex (place). During transformation, one pebble is lost as toll and only one pebble reaches the end. The lower bounds and upper bounds of energy levels were investigated for various types of simple and undirected graphs through pebbling concept.

Psosets and trellises are generalizations of posets and lattices respectively. In fact, these notions are introduced independently by E. Fried and H. L. Skala. It is well known that a graph can be used to describe a partial order. In this paper, the concepts of modular, weakly distributive and normal trellises are introduced. We have proved that a trellis satisfying sheering property is modular. It is also proved that every strongly connected trellis is nonmodular. It is shown that every separating element of a trellis is modular and every modular element is weakly separating. Well-known result of M.H. Stone namely "Every maximal ideal of a distributive lattice is prime" is generalized to trellises. It is proved that a relatively complemented trellis is a lattice if and only if it is normal.

This paper concerns the oscillatory behavior of the solutions of the third-order neutral differential equation with continuously distributed delay. We prove many new sufficient conditions which ensure that every solution to be either oscillatory or converges to zero asymptotically. Examples dwelling upon the importance of our theorems are also included.

In this work, the homotopy perturbation method together with the natural transform are applied to solve some nonlinear space-time fractional Fokker-Planck equations. The numerical and exact solutions in examples are shown to support our results.

This paper presents a new notion of complex cubic interval valued intuitionistic fuzzy set (CCIVIFS) which is an extension from the innovative concept of a cubic interval valued intuitionistic fuzzy set (CIVFS). The novelty of CCIVIFS is to achieve more range of values with the combination of interval-valued membership, interval-valued non-membership and fuzzy membership. We define some basic operations namely complement, union, intersection and notions of $\tilde{\alpha }$-internal, $\tilde{b}$-internal, $\tilde{\alpha }$-external and $\tilde{b}$-external complex cubic interval valued intuitionistic fuzzy set are introduced. Also P-union, P-intersection, R-union and R-intersection of $\tilde{\alpha }$-internal and $\tilde{b}$-external complex cubic IVIF sets are discussed. Furthermore, a group decision-making method is discussed to illustrate the applicability and validity of the proposed approach.

In this paper, we use the new modification of the Adomian decomposition method (NMADM) to formulate a solution of some weakly singular Volterra integral equations. In some cases, Taylor's series is applied to simplify the formula. Some examples are given to illustrate the applicability and effectiveness of this method.

Domination is an important theoretic concept in graph theory. Various types of domination have been studied By [J, K] - Set domination, A subset D ⊆ V in a graph G = (V, E) is a [J, K] - Set if every Vertex ν ∈ V−D, J ⩽ |N(ν) ∩ D| ⩽ K for non negative integers J and K, that is every vertex ν ∈ V−D is adjacent to at least J but not more than K Vertices in D. The domination number of G is denoted by γ_[J,K](G), which is the minimum cardinality of a dominating set G. In tis paper the [J, K] - domination number of some special graphs and its application ave been studied.

The present article deals with the dispersion of a solute in peristaltic system. This mathematical model provides the analytical solution of electro-magnetohydrodynamic flow of biofluids through a channel. Treating blood as a Jeffrey fluid and considering homogeneous chemical reaction, the closed form of solution of effective dispersion coefficient is obtained by using Taylor's limiting condition and long wave length approximation. The impacts of physiological parameters such as the electro osmotic velocity, electro kinetic, Jeffrey fluid parameter and Hartmann number on the Peristaltic movement have been investigated. It is found that the average equivalent dispersion coefficient is reduced with respect to the enhancement of homogeneous chemical reaction parameter and Hartmann number. It is pertinent to point out here that the electro osmotic velocity and electro kinetic parameter help to enhance average equivalent dispersion coefficient in comparison with the absence of applied electric field. The present analytical study provides useful information to artificial bio-processors.

Discontinuous system is playing an increasingly important role in terms of both theory and applications. In this paper, we are concerned with discontinuous BAM (bidirectional associative memory) neural networks with time-varying delays. Under the basic framework of Filippov solution, by means of differential inclusions theory, inequality technique, fundamental solution matrix of coefficients and the non-smooth analysis theory with Lyapunov-like approach, some new sufficient criteria are given to ascertain the existence and globally exponential stability of the anti-periodic solutions for the considered BAM neural networks. Simulation results of two topical numerical examples are exploited to illustrate the improvement and advantages of the established theoretical results in comparison with some existing results. Some previous known results are extended and complemented.

In this paper, Inspired by the Fuzzy regular grammar, a new approach is proposed as the Intutionistic fuzzy regular grammars.

Consider a two commodity continuous review inventory system with a finite number of homogeneous sources generating demands. The maximum storage capacity for the commodity - i is S_i(i = 1, 2). We adopt a joint reordering policy for placing orders. The lead time for the delivery of orders is assumed to have an exponential distribution. An arriving demand receives either commodity - 1 or commodity - 2 according to a Bernoulli trial. The commodities are assumed to be substitutable in the sense that during the zero stock of any commodity, the demand for that commodity can be met by the unit of the other commodity. The server goes for a vacation of an exponentially distributed duration whenever the inventory level of both commodities reaches zero. If the server finds empty stock when he returns to the system, he immediately takes another vacation. The demands that occur during stock-out period or during the server vacation period enter into the orbit of finite size. These orbiting demands retry for their demand after a random time, which is assumed to be an exponential distribution. The joint probability distribution of the inventory level and the number of demands in the orbit is obtained in the steady state case. Various system performance measures in the steady state are derived and the long-run total expected cost rate is calculated.

In this article, we have investigated the peristaltic transport of electro-osmotic flow of Jeffrey fluid in an asymmetric channel, in which the walls are modulated by the peristaltic array of patches. In the presence of Electrical Debye Layer (EDL), the Poisson Boltzmann equation for the electrical potential within the micro channel is considered. To evaluate the electrical potential, Debye-Huckel linearization is employed the governing equations are modeled and reduce by small Reynolds number and long wavelength approximation and solved the exact solution. The axial fluid velocity, temperature, pressure gradient, pressure rise and stream functions are discussed with the effects of pertinent parameters (Hartmann number, Phase angle, relaxation time parameter) through the graphs.

In this paper, the Adomian decomposition method together with a property of nested integral are used to solve a class of coupled systems of first-order ordinary differential equation. Some examples are given to show the effectiveness of this method.

In this article, we investigate the existence results, with multi-point and integral boundary conditions, for Caputo-Hadamard fractional diσerential equations (CHFDEs) and inclusions. To get the desired results, which are clearly illustrated by examples, we use standard fixed point theorems for single-valued and multi-valued maps.

This paper deals with nonlocal conditions of impulsive differential equations with control. Here, we structure the measure of noncompactness and its properties in the space of piecewise continuous functions. Then, we acquire the controllability of impulsive differential equations with nonlocal conditions via compactness condition, Lipschitz conditions by using the Darbo-Sadovskii's fixed point theorem and the property of noncompactness.

Grains have enacted a supreme role in human history and grain agriculture. Cereal grains are the worlds most substantial origin of food energy. The loss of grains can occur in three stages which are Pre-harvest, harvest and Post-harvest stages. Post-harvest losses take place during the time of harvest and the stage of human consumption. The losses can occur at the process of transportation, processing, storage and also by insects attack. In many developing countries the post-harvest losses are normal. In grain storage, several methods are being used to detect insects. But methods which are efficient and also time saving are very much needed. So, researchers have advanced many detection techniques to find insects in the stored grains. The weighted correlation coefficient using entropy weights give more enlightenment to solve many prevailing problem in real life. The encouragement of this research work is to interpret the sellers perspectives of insect detection technique for stored grains.

In this manuscript, we have investigated the peristaltic transport of Oldroyd-B fluid in an inclined channel. The channels are taken asymmetric into the account and subjected to rotation of the presence of a magnetic field and gravity field. The governing equations of Oldroyd-B fluid are derived and the constitute nonlinear equations are reduced under the consideration of large wave length and small Reynolds number approximation. The exact solution of the equations is derived. The consequences of pertinent aspects of axial velocity, pressure gradient, pressure rise and stream functions are discussed through the graphs.

One of the most important reasons of car accidents are collisions with vehicles that are not visible to a driver. This is why driver warning systems are developed. The main threat for a driver on the highway comes from the surrounding vehicles especially when the driver is not aware of the close presence generally known as driver's blind spot. An area in and around the vehicle that cannot be directly observed by the driver are known as blind spots. Image processing plays a vital role in this scenario to safe guard drivers from sudden obstacles and blind spots. The pre-processed sequences of images acquired using front and rear camera of a vehicle are considered to train the case base reasoning (CBR) model, which detects the presence of dangerous objects in the blind spot area. To distinguish near and far obstacles, the same CBR model is used with a specified threshold in the vehicle blind spot area. The proposed knowledge based obstacle information system obtains promising results with standard blind spot camera which can improve safety of the driver and has the potential to be applied in vehicular applications for the detection of obstacles and blind spot area.

In this paper, we first introduce the concept of Q-Pythagorean fuzzy soft expert set(QPFSES) which combines Pythagorean fuzzy set and soft set expert set. We also define some operations namely complement, union, intersection and study some of their properties. Further an approach for solving multi-criteria decision making (MCDM) problem is explored by applying Q-Pythagorean fuzzy soft expert set and an example is provided to illustrate the application of the proposed method.

In this paper, the problem of finite-time stability of neural networks with time varying delay is considered by using improved reciprocally convex inequalities and some integral inequalities, combined with Wirtinger's inequalities and some useful integral inequality. New sufficient conditions for finite-time stability are established to guarantee finite-time stability for the system are given in terms of linear matrix inequalities(LMIs). Numerical examples are given to illustrate the effectiveness of the obtained result.

In this paper, the global exponential stability for the neutral-type inertial bidirectional association memory neural networks with time-varying delays is considered. In our study, the lower and upper bounds of the activation functions are allowed to be either positive, negative or zero. By constructing new and improved Lyapunov-Krasovskii functional and introducing free-weighting matrices, a new and improved delay-dependent the neutral-type inertial bidirectional association memory neural networks with time-varying delays is derived in the form of linear matrix.

This paper is concerned with the problems of robust stability analysis and H_∞ performance for the uncertain neutral systems with mixed time delays. By constructing an augmented Lyapunov Krasovskii functional with quadruple integral terms, some sufficient criteria are provided in terms of linear matrix inequalities (LMIs). The goal of this paper is to establish some conditions to guarantee the system is robustly stable with a prescribed H_∞ performance level for all uncertainties.

In the present work, we attempt to analyze the discrete form of Leslie type predator-prey system with the extension of nonlinear type harvesting of predators. The proposed model is obtained with the help of theory of piecewise constant argument for differential equations. We give the local stability properties of all possible non-negative fixed points. Also, our study reveals that the discrete system admits two bifurcations which are flip and Neimark-Sacker by making the use of center manifold argument and bifurcation theory, where the harvesting parameter is varied in order to take place of such bifurcations. Some simulations are carried out to depicts the obtained analytical results such as bifurcation plots and phase portraits. Also, it can be confirmed from numerical simulations that the considered system exhibits chaotic behavior for smaller values of harvesting parameter and becomes stable for larger values of same parameter. The largest Lyapunov exponents are plotted to show the sensitivity of chaotic regime.

In this paper, concerning non-local multi-point and integral boundary conditions, we investigate the existence and uniqueness of solutions for Hadamard fractional diσerential equations (HFDEs) and inclusions. In the case of equations, we use the Krasnoselskii fixed point theorem for the sum of two operators and Banach fixed point theorem, and Leray-Schauder's alternative for multivalued maps and the fixed point theorem attributed to Covitz and Nadler for multivalued contractions for inclusions. Examples are given to clarify our main results. Finally, we discuss some variants of the given problem.

In this research, we deals with the quasilinear third order delay difference equations of the term ${\rm{\Delta }}(\rho (n){({{\rm{\Delta }}}^{2}y(n))}^{\alpha })+q(n){y}^{\alpha }(n-\sigma )=0,\phantom{\rule{0.25}{0ex}}n\geqslant {n}_{0}$. We establish the sufficient conditions for all solutions of studied equation to be oscillatory or almost oscillatory. The criteria improve and complement of existing results. We provide some examples to describe the major results.

Recently, G. Mahadevan et.al. proposed the idea of ATES domination number of a graph. In [6] A set S ⊆ V is said to be At most twin extendable separated dominating set, if for every vertex 1 ≤ |N(V) ∩ S| ≤ 2, v ∈ V − S and < V − S > is a perfect matching. The minimum cardinality taken over all At most twin extendable separated dominating sets is called At most twin extendable separated domination number of a graph and it is denoted by ATES (G). In this article, we analyze this number for some specializes types of graphs.

In this paper, a non-linear mathematical model is formulated and analyzed to understand the dynamics of plant disease in presence of predators. Here predators act as biological control agent that reduce the vectors carrying the disease pathogen. The mathematical model is formulated using system of delay differential equations by considering two delays. The delays are time taken for the plant to become infected after contagion and time taken for the insect to become infected after contagion. The existence and stability of different equilibria of the model are discussed in detail. The basic reproduction number R₀ is computed. The Routh-Hurwitz criteria is used to investigate the stability of the disease-free equilibrium and the endemic equilibrium in absence of delay. The stability of endemic equilibrium is also investigated in presence of delay. The occurrence of Hopf-bifurcation is demonstrated by considering the delay as the bifurcation parameter. The critical values of the delays are obtained which preserve the stability of the endemic equilibrium point. The model system shows an oscillatory behavior beyond this critical values of delays. Numerical simulation is also performed to support the analytical results. It is found that biological control has positive impact on reducing the transmission of plant disease.

This paper analyzed the heat transfer with impact of slip condition an oscillatory blood flow through a stenosed artery. We derive the equations for the mixed convection problem of blood flow as nonlinear partial differential equations and the exact solutions solved by analytically. The Effects of various parameters particularly magnetic field on the blood flow through stenosis have been examined. The computational results are presented graphically for the temperature, velocity, flow rate and skin friction.

In this paper, we study the characterization of uniform cellular automata with the restricted vertical neighborhood and hybrid cellular automata with both restricted vertical neighborhood and Von Neumann Neighborhood using reflecting boundary condition over the eld ₂. The transition rule matrix for uniform and hybrid cellular automata with reflecting boundary condition is obtained and also reversibility of the uniform cellular automata is studied.

Child mortality is one of the important factors to reflect sustainable development for any nation. It is common sense now that child mortality rate depends on medical services platform and its quality. To predict model under-five child mortality rates in India, multiple linear regression analysis was used. Identifying the factors that affects the under-five child mortality. To examine the relationship between all the variables along with recognize the problem of multicollinearity in the variables. In this study our fitted multiple linear regression model found that under five child mortality rates in India are influenced by tuberculosis case detection rate, measles death rate and hepatitis immunization rate. To choose appropriate model ACI score is used.

The nonlinear evolution equations of fourth-order have been established for two surface gravity waves in infinite depth of water including the effect of air flowing over water. In the present paper, we have applied a general approach depending upon the integral equation due to Zakharov. Based on these equations, the stability analysis has been studied in the appearance of a uniform gravity wave packet with another wave packet of the identical group velocity. Graphs have been drawn for the instability growth rate of the uniform wave packet with shorter wave number versus the perturbed wave number for several values of the amplitude of the wave packet of larger wave-number and several values of wind velocity. We have observed from the figures that the instability growth rate of the second wave packet enhances with the enhancement of nondimensional wind velocity for the settled value of the amplitude of the first wave packet.

In this article, we present solution of partial differential equations by using Mohand transforms. We also present examples to illustrate the preciseness and effectiveness of this.

Differential equation is important in explain the results, which has been applied in science, physics and engineering etc. In this paper, the author study a comparison between finite difference method and Laplace transform for solve the differential equation by The finite difference method using forward differenc backward difference and central difference and also present examples to illustrate the preciseness of this method.

A very large section of the Indian population depends on farming to meet their ends. But due to several reasons - natural or man-made, not limited to weather, proper irrigation mechanisms and finance, many a section of this society are often unable to reach their expected sustenance. A proper guidance mechanism that helps the farmers or aspirants select the suitable choice of crop to be cultivated in an area based on the climatic and soil conditions will increase the agricultural productivity per unit of land. In this paper, we propose a predictive system that aids the farmers in crop selection based on different climatic and soil parameters available from a dataset pertaining to Indian subcontinent. An IOT system will determine the climatic (temperature, humidity etc) and soil (pH, moisture, etc) conditions in the area of choice. This is input to the predictive system which predicts the choice of crop. The developed system can be adopted to achieve a healthy crop growth that can be adapted by agricultural practices.

Ensuring authentication in the Internet of Things (IoT) environment is a crucial task because of its unique characteristics which include sensing, intelligence, large scale, selfconfiguring, connectivity, heterogeneity, open and dynamic environment. Besides, every object in the IoT environment should trust other devices with no recommendation or prior knowledge for any network operations. Hence, those characteristics and blindness in communication make security violations in the form of various attacks. Therefore, a trustbased solution is necessary for ensuring security in the IoT environment. Trust is considered as a computational measure represented through a relationship between trustor and trustee, explained in a particular context valued through trust metrics and evaluated by a trust mechanism. The proposed logistic regression-based trust model provides an efficient way to identify and isolate the misbehaving nodes in the RPL (Routing Protocol for Low Power Lossy Networks) based IoT network. It is one of the popularly used routing protocols in IoT, that builds a path especially for the constrained nodes in IoT environments. However, it is vulnerable to many attacks. The proposed model classifies and predicts the node's behavior (trusted or malicious). This model uses the logistic regression model to predict the node's behavior based on the integrated trust value which is computed from the direct trust, reputation score, and experience trust. It is primarily designed to address the black hole attack in the IoT environment. The mathematical analysis shows the possibility of the proposed work and the simulation results show the proposed model is better than the existing similar work.

In the Internet of Things based military environment, to achieve an assigned task without compromising security concern is a challenging task. Resource-constrained devices, Self-organized, disseminated nature of sensor nodes, unstable topology environment, open wireless medium, and shared network environment make IoT differ from other networks. All together leads to security threats to the IoT environment. The success of any IoT based application depends on effective communication among the devices that can be achieved by routing protocols. Typically, they designed to cope with fruitful communication but in effect, they might be targeted and affected by mischievous devices. Blackhole devices are such devices that aim to disturb the normal routing operations. But the identification of trusted devices that means authentication needs to be provided for successful task completion. At present, trust management plays an important part in prediction construction and appropriate for resource-strained devices. In this article, a multi-dimensional trust-based security model is proposed to guarantee authentication by avoiding blockhole devices based on direct, indirect, sense-making, social, and stereotypes. In addition, the q-learning mechanism is used to enhance the proposed method. The simulation study represents the applicability of the projected model.

Multi-storey buildings are emerging because of the lack in land availability within urban areas. Mostly, tall buildings are irregular in plan and more complex to wind action. In the present scenario, it is important to study the wind structure interaction for irregular plan shape tall buildings. This paper is focused on understanding the behaviour of pentagon plan shape building under wind load at different wind incident angles 0°, 45°, 90°, 135° and 180°. The wind behaviour is studied using Computational Fluid Dynamics (CFD) and turbulence model k- is used for external flow simulation around the tall buildings. The building models are scaled in the ratio 1:300 and wind velocity at inlet is scaled in the ratio 1:5 respectively. From the results, external pressure coefficient on various faces of the buildings, drag coefficient and lift coefficients are determined for pentagon shape building. The maximum positive external pressure coefficient (C_p) is 0.446 had occurred in Face A at 180° wind incident angle and the maximum value of the negative external pressure coefficient (C_p) is 0.388 had occurred in Face D at 135° wind incident angle.

Agriculture is the major factor contributing to Indian Economy. According to the current statistics, its contribution to GDP sector is 17.9%. Technical advancement in agricultural domain will produce more agricultural products without any wastage of money, time and manpower. Nutrients play a major role in plant growth. Lack of nutrients leads to reduced crop yield and plant growth. In this work, we are trying to create an artificial neural network model to recognize and classify the nutrient deficiency in tomato by examining the leaf characteristics. This will help farmers to adjust the nutrient supply to the plant. If soil lacks a specific nutrient, it will reflect in the physical characteristics of a leaf. The color and shape of a leaf are the two major features used for identifying the nutrient deficiency. The comparison of different segmentation schemes like hue based and threshold based schemes shows their influence in the performance of the proposed system. The influence of different activation functions in the artificial neural network is also studied in this work. The results show that the proposed method was able to classify and identify nutritional deficiencies with high accuracy.

Falling losses from aquatic disease is the main public condition goal in developed countries. The present study terms the application of Physical Sciences and Environmental Sciences techniques to solve the real-life problem associated with the society. Water samples are taken from a river, pond, bore well, and municipality at Kabisthalam in Kumbakonam Taluk, Tanjore District, Tamil Nadu, South India. The current work defines the expansion of mathematical typical to expect the interaction parameters which were used to determine the quantitative characteristics of the water. Analysis of Variance (ANOVA) was employed to identify the level of importance in interaction parameters on their characteristics. The effect of these parameters on interaction has been investigated using experimental designs. The new results have been correlated using the Fuzzy Evidence Theory. The salient aspect of the work is that a very simplified analytic output of the fuzzy model is achieved when all fuzzy sets in the fuzzy partition of the output space have the same power (the area under the membership function), and the determination of basic probability assignments associated with fuzzy Dempster-Shafer belief structure using fuzzy focal elements.

The combined effect of centrifugal acceleration and time-varying boundary temperatures on the onset of convective instability of a rotating magnetic fluid layer is investigated by means of the regular perturbation method. A perturbation expansion in terms of the amplitude of applied temperature field is implemented to effectively deal with the effects of temperature modulation. The criterion for the threshold is established based on the condition of stationary instability manifesting prior to oscillatory convection. The modulated critical Rayleigh number is computed in terms of Prandtl number, magnetic parameters, Taylor number and the frequency of thermal modulation. It is shown that subcritical motion exists only for symmetric excitation and the destabilizing effect of magnetic mechanism is perceived only for asymmetric and bottom wall excitations. It is also delineated that, for bottom wall modulation, rotation tends to stabilize the system at low frequencies and the opposite is true for moderate and large frequencies. Furthermore, it is established that, notwithstanding the type of thermal excitation, the modulation mechanism attenuates the influences of both magnetic stresses and rotation for moderate and large frequencies.

The temperature increase of the PV panel reduces the electrical efficiency of the module. In order to boost electrical efficiency, the temperature of the PV panel is decreased by working fluids such as water and water based TiO₂-MWCNT hybrid nanofluid. The pattern of the absorber is spiral. The spiral flow absorber collector is a steady loop. This model was implemented to determine the total heat gain and total combined efficiency of the PV module. The findings show that total thermal performance, optimum thermal output and electrical performance achieved by TiO₂ –MWCNT nanofluid is more compared with water. In the nanofluid coefficient of convective heat transfer is higher than that of the base liquid at the same mass flow rate. For a mass flow rate of 0.01 kg/sec, the maximum thermal efficiency and electrical efficiency obtained are 52.8 per cent and 8.6 per cent, respectively, relative to the simulation results.

Two and Three chamber expansion muffler are commonly used in light category vehicle for meeting the noise level legislature requirement. The Helmholtz resonator and expansion chamber are used in exhaust muffler to attenuate the noise in low and middle frequency range. In this work, the effect of expansion chamber size on back pressure is determined using CFD and the same geometry were used to study the acoustic attenuation performance using FEA in the frequency range of 0 to 3000 Hz. Regarding the size of individual expansion chamber there is about 17% increase and decrease in size from base model geometry were considered for performance comparison in both two and three chamber type of muffler. It is found that minimum back pressure of about 241 Pa is observed for 2 chamber base model (2C-B) with slightly higher turbulent kinetic energy value of 77.53 J/Kg. The sound pressure level (SPL) at outlet pipe is less for 3 chamber mufflers and the obtained value is less than 120 dB for most of the frequency range of 0 Hz to 3000 Hz. Similarly transmission loss (TL) is higher for 3 chamber mufflers and the value remains same for 0 to 1600 Hz frequency range and peak fluctuation occurs at higher frequency. The obtained results shows that 3C-A model is having higher noise attenuation performance with back pressure value within acceptable limit.

This research work deals with more proficient and at ease to design the fuzzy logic controller (FLC) meant for course-changing. A new system in tuning a rule base in fuzzy controller system. Agreeing to the modification status of system error, the proposed real-time tuning algorithm is used in tuning the subsequent portion of fuzzy values, later the rule base is controlled. This proposed work also links the more performance of FLC at several working situations with conventional PID controller. In our proposed method we joined the PID with Fuzzy logic to build the strong and adaptive controller. The Simulation results are valuable to demonstrate this method.

Prevalence of crop diseases is a major hindrance for successful crop production. These diseases can be identified in less time and more accurate using Machine Learning (ML) strategies as compared to any manual approach. Agronomy plays a key role in anticipating crop diseases at an early stage. With the advent of computer vision, plants can be classified as diseased or healthy by extracting architectural characteristics of a leaf using various image processing techniques. Support Vector Machines (SVM) classification technique is used in distinguishing between diseased and healthy leaf from the datasets that are publicly available. SVM method exhibited high fitting and predictive precision. The proposed paper is organized in various steps such as identifying the features, extraction of features using a computer vision technique known as Scale Invariant Feature Transform (SIFT), model training and testing. Predominantly, crop diseases on a larger scale are predicted by harmonizing speed and accuracy using computer vision and machine learning strategies.

A different Mn_x(x= 0.03, 0.05, 0.07) doped on CuO_1-x has been successfully synthesised by a co-precipitation method by maintaining a pH-12. The nature of Mn doped CuO nanoparticles has been characterized with the help of X- Ray Diffraction (XRD). The Mn in the lattice sites of CuO gives the monoclinic crystal structure with C2/c space group which has been confirmed through JCPDS card no: 05-0661. The morphology variations with Mnx doping have been examined with the help of field emission scanning electron microscope (FESEM) and Energy Dispersive X-Ray Spectroscopy (EDS). Additionally, band properties have also been noticed via Ultraviolet-Visible (UV) Spectroscopy. The band gap of material has been calculated as 2.39 eV, 1.96 eV and 2.25 eV for energy harvesting modelling through MATLAB with temperature difference behaviour of material. The thermodynamic modelling has been used for energy harvesting application with the help of MATLAB and the Seebeck coefficient has been calculated for thermoelectric modelling of CuO-Mn_x.

Mixture of coherent state with thermal noise is known as the Glauber Lachs state, which is taken into consideration. Nonlocal photon addition is imposed on the two mode Glauber Lachs state by the application of bosonic creation operators. This nonlocal photon addition induces nonclassicality, revealed in the single mode and two mode squeezing properties. The ratio of the coherent noise to thermal noise is the key factor in observing the nonclassical features. The tolerance limit of the noise for the nonclassicality is discussed in single mode squeezing and two mode squeezing quadrature operators. The results show that the squeezing properties are less pronounced even for the low level of thermal noise.

We consider the simplest case of Rutherford scattering, i.e. the head-on collision, where the projectile is treated quantum mechanically. The convexity of repulsive Coulomb force invokes a disagreement between the Ehrenfest's and Hamilton's dynamics. We show that the quantum projectile cannot approach as close as the corresponding classical one, and that the average distance of closest approach depends on the position spread of the wave function describing the projectile.

Dipole moments have been determined by using the mixtures of diluted solutions of aniline, o-chloro aniline, p-chloro aniline, ethanol, 2-butoxy ethanol and 2-methoxy ethanol in carbon tetrachloride at 30° C based on Debye's polarization method and Huysken's method. The results are interpreted that the complex dipole moment for the halogen substitution of acceptor complexes is greater than the mono substituted acceptor complexes. But the case is reversed in halogen substitution of donor complexes.

The extension of Parikh vector is Parikh matrix which is a useful tool in arithmetizing words by numbers. Another interesting problem is the extension of Parikh matrix of a words to 2D words. However, Parikh matrix fails to tell about the number of subword occurrences in 2D word. Therefore, in this paper we introduce the notion of generalized Parikh matrix of 2D words which fulfill the number of subwords occurrences in an 2D words and also we obtain the properties of the generalized Parikh matrices.

In this paper, we introduce gp^* -exterior and gp^*-frontier and some of its basic properties.

Recent studies involve various approaches to establish a generating set for cyclic codes of arbitrary length over the class of Galois rings. One such approach involves the use of polynomials with minimal degree corresponding to specific subsets of the code, defined progressively. In this paper, we extend this approach to obtain a set of generators of cyclic codes over finite chain rings. Further, we observe that this set acts as a minimal strong Gröbner basis(MSGB) for the code.

In this paper the Fuzzy Regularly closed subsets have been discussed with the help of the Fuzzy Topological Space defined by Michálek. Also we have discussed some characterstics of Fuzzy Regularly Closed sets.

Linear complementary dual(LCD) codes are being utilized to protect cryptographic implementations from side-channel and fault attacks. In this work, LCD codes over the ring Z₄ are examined. It is observed that an LCD cyclic code over Z₄ of odd length is always reversible. However, the converse of this result does not hold. A suitable example to validate this statement is presented. Further, a necessary and sufficient condition for a reversible cyclic code of odd length to be an LCD code is obtained. Finally, it is found that among cyclic codes of length 2^k, no non-trivial LCD code exists.

A new labeling named 'Sum Modulo Three' (SMT) is introduced and its verifications on a general single star and general two star are provided. Also an application using the labeling on a general two star is presented.

In this article, some fixed point theorems of contraction mappings on cone metric spaces are obtained. Moreover, the concept of weak convergence in metric spaces is extended to cone metric spaces, and some results on weak order convergence of fixed point iterations of various types of contraction mappings on cone metric spaces are obtained.

Latest generality appearance of nano weakly πg-closed sets, nano weakly πg-open sets which are weaker forms of nano πg-closed sets, nano πg-open sets respectively. The relationships among them related generalized closed sets is also investigated in this paper.

Motivated by some results on derivations on rings and the generalizations of BCK and BCI-algebras, in 2019, P. Ganesan and N. Kandaraj introduced the notion of derivations on BH - algebras. In this paper, we study the notion of Composition of f - derivations on BH – algebras and investigate simple, interesting and elegant results.

In this paper we introduce the concept of mid-units in seminearrings. We obtain some results concerning mid-units in seminearrings. In particular, we study the relationship between mid-units and idempotents in seminearrings. We derive a necessary and sufficient condition for duo seminearrings to have a mid-unit.

The bipolar fuzzy theory is a very effective tool for addressing real life problems in various field such as disease diagnosis, spatial information, image processing and engineering etc. The novel concepts of bipolar fuzzy centred system and bipolar fuzzy centred texture di topological spaces are introduced. Then we established the significance of bipolar fuzzy centred texture compactness, bipolar fuzzy centred texture nearly compactness and discussed some interesting characterizations on it. Finally, defined the idea of bipolar fuzzy centred texture nearly stable and bipolar fuzzy centred texture nearly co stable and its properties are also studied.

In this paper, we prove some continuation results based on essential maps in −uniquely geodesic spaces, which are generalizations of the existing results in Banach spaces. Also, we obtain Leray Schauder principle in −uniquely geodesic spaces which generalizes Leray Schauder principle in the setting of Hyperbolic spaces.

In recent times, the internet of things has gained more popularity. The internet of things connects people, objects and machines apart from distance through cloud based internet. In this paper, we have introduced the smart fuzzy graph along with some basic properties and related concepts. The aim of this paper is to solve some authentic real life problems using smart fuzzy graph.

In this work, we construct a complexity together with the folding method to obtain a rank formula for HNN-extension with finite edge group.

The purpose of this paper is to discuss about 𝑸 T_αm continuous functions and initiate new class of function called 𝑸 T_αm irresolute function. Also a new class of 𝑸 topological space called 𝑸 T_αm Highly Disconnectedness Space is introduced. On this basis, some interesting properties of these spaces have been obtained.

In this paper, The concept of topological structure on Mechanical is introduced and some properties are studied.

This paper deals with the properties of ideals in seminearrings with special reference to right duo seminearrings. We formulate the concept of prime ideal and minimal prime ideal in a seminearring. In the case of Noetherian right duo seminearring, we derive some additional properties.

A subgroup G of the symmetric group S(P ) of all permutations of a set P is called L_f -representable on P if there is an L-topology δ on P with the group of L-homeomorphisms of (P,δ) = G. In this paper we study the L_f -representability of some subgroups of the symmetric group.

Fuzzy rough set is a pair of lower and upper approximations of fuzzy set in a fuzzy approximation space. This paper studies the extension of fuzzy rough prime and semi-prime ideals in semigroups. Then we introduce the composition theory on fuzzy rough set. Finally some new characterization of semigroups by the properties of composition on fuzzy rough ideal extension are given.

In this paper, we introduce the notions of intervalvalued rough (∈^*, ∈^* ∨ q^*)-fuzzy subsemigroup, intervalvalued rough (∈^*, ∈^* ∨ q^*)-fuzzy ideals, intervalvalued rough (∈^*, ∈^* ∨ q^*)-fuzzy bi-ideal, intervalvalued rough (∈^*, ∈^* ∨ q^*)-fuzzy interior ideal and intervalvalued rough (∈^*, ∈^* ∨ q^*)-fuzzy quasi ideal as a further generalization of ideals in semigroups and study the properties of these structures.

Given a non-empty subset X of the real line and a self map G on X, the functional equation representing G as an infinite linear combination of iterations of a self map g on X is known as the series-like functional equation. The solutions of the series-like functional equation have been studied only for the class of continuous strictly monotone functions. In this paper, we prove the existence of solutions of series-like functional equations for the class of continuous non-monotone functions using characteristic interval.

The aim of this work, is to introdued sufficient conditions for prove the existence and uniqueness of fixed point of the Hardy-Roger contraction in complete complex valued S_b-metric spaces. Our results extend and improve the results of Riyobarta N. et. al[10].

The properties of fuzzy path covering space, fuzzy lifting from an arbitrary fuzzy map to a fuzzy path covering map are discussed in this paper. Also the properties of fuzzy path covering space and fuzzy pointed topological space in fuzzy Peano space are discussed.

This paper is the study of Fuzzy supra hyperconnected spaces (denoted by FSHS). After studying the characteristic of FSHS concerned with different concepts. The relationship between these concepts is investigated. The properties of FSHS are studied.